Coils design rules

To produce a field B of 1 weber/m2 (10 kilogauss) in a gap of 10 cm length, the number of ampere-turns required is 7.95 x 10^4 ... At 18 kilogauss ... the observed value of B is 0.73 of that predicted.

Livingston & Blewett, Particle Accelerators (1962) — p. 258-260

Tabletop: At the reference machine's 5.9 kG the linear formula is trustworthy: ~1.4e4 ampere-turns for a 3 cm gap; headroom for a hotter field on the next machine is cheap until ~10 kG, expensive after.

a common phenomenon ... is to find the median plane dished into a shallow saucer shape caused by asymmetries in the magnet iron or of the reinforcing iron in the foundations ... At MIT such a 'dished' median plane was corrected by connecting an external resistor in parallel with one of the coil layers.

Livingston & Blewett, Particle Accelerators (1962) — p. 288

Tabletop: Rebar in the floor or a nearby steel bench can dish an H-frame tabletop field; check for it and trim electrically rather than re-machining.

The magnet consists of coils of hollow copper tubing wound on a two-ton core of mild steel ... These deliver to the magnet 20 kilowatts of electric power, which is dissipated by water circulating through the coils.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 6-7

Tabletop: Sets the scale of the jump from the reference machine's 0.59 T solid-copper-tubing magnet to a 1.7 T machine: hollow conductor and real water cooling become mandatory, and power goes to tens of kW.

we used the basic equation for an electromagnet... we decided a 2.13'' gap a reasonable size... we then concluded that we needed 720 turns to reach 1.6T.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Tabletop: Same sizing equation the reference machine's 538-turn magnet obeys; lets them trade gap, turns, and current for any next machine's target field on one line.

Bair = mu0 NI / (g + lambda/mu); ... Approximation ignoring iron reluctance (lambda/mu << g): NI = B g /mu0

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 25

Tabletop: The correction term is exactly what bends the reference machine's excitation curve at high current; measuring B vs I against this formula reveals where the yoke saturates.

Given the field = B0, pole width = a, Magnet Length = L and ramp time dt, the only design option available for changing the voltage is the number of turns, N.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 12-16

Tabletop: Quick check on a next machine's supply matching: stored energy in a 10 inch, 1 T, 5 cm gap magnet is ~100s of joules, and turns count trades current for voltage against whatever surplus supply the builder finds.

Note that all regions must close, that is the first and last coordinates are equal ... Negative currents in the right hand coil gives positive flux on the horizontal centerline.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 9

Tabletop: The two mistakes that make a first POISSON run fail; also shows amp-turns (not turns and amps separately) are what the model needs.

efficiency ~ 0.98 For magnets with well designed yokes.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 4-6, 12

Tabletop: Lets the builder size a next machine's amp-turns to ~2% accuracy with hand arithmetic before any FEA.

The electrical bussing connection creates a loop around the beam line, resulting in a small solenoidal field... the in and out conductors should be placed close to each other.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 24-26

Tabletop: Cheap to get right on a next machine: dress the coil leads as a twisted/adjacent pair and keep supply cables from encircling the chamber.

coil cooling estimation: dT(C) = 60*P(kW)/(4.19*N(l/min))

Zaremba, Magnets for Cyclotrons (2005) — p. 30-32

Tabletop: The cooling formula is immediately usable: a next machine's 5 kW coil at 4 L/min runs ~18 C water rise; the flutter formulas matter only if the builder adds sector (AVF) pole faces.

where h is the magnet gap height in [m] ... eta is the efficiency (typically 99%), mu_0 is the permeability of free space ... Note that Eq. (5) is only approximate and neglects fringe fields and iron saturation.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 15

Tabletop: First-cut sizing for a next machine: at a 2 cm gap and 1.0 T you need ~8000 A-turns per pole, which sets conductor/current density before any FEMM run.

U_magnet = U_gap + 2 U_coil + U_yoke = B^2/(2 mu_0) (V_gap + 2 V_coil/6 + (1/mu_r) V_yoke)

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 18

Tabletop: Tells you the inductance and therefore how fast a bench supply can ramp the magnet and how big the flyback/crowbar protection must be.

l_avg = pole perimeter + 8 x clearance between pole and coil + 4 x coil width

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 27, 33

Tabletop: Gives copper length, hence resistance and power, straight off a sketch - exactly what a garage builder needs before ordering tubing.

the maximum current density for voluminous coils which are almost entirely enclosed in the magnet yoke should not exceed 1 A/mm2 ... The current density in direct water-cooled coils can be typically as high as 10 A/mm2.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 28-29, 31

Tabletop: The reference machine's 538-turn solid copper tubing coils sit in the air-cooled regime; this rule says they must stay under ~1-2 A/mm^2 unless they switch to hollow conductor with water flow.

The velocity of the cooling medium ... should be sufficiently high to guarantee a turbulent flow but low enough (u_avg <= 5 m/s) to avoid erosion and vibration. A maximum permitted temperature of less than 60 C on the coil surfaces was found to be good practice.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 31

Tabletop: Gives hard numbers for a home chilled-water loop: exceed 5 m/s and you erode the tubing; exceed 60 C and the insulation ages fast.

Q_water = 2.388 x 10^-4 P/dT ... d = 5.59 x 10^-3 (P/(dT Kw))^0.368 (l/dp)^0.21

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 32-34

Tabletop: Lets the builder compute the hollow-conductor bore and pump requirement for a next machine's 5-20 kW magnet with a spreadsheet, no CFD.

NI_dipole = Bh/(eta*mu0), where the magnet efficiency, eta... The magnet efficiency for a well designed yoke is eta >= 98%.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 116-117, 129

Tabletop: One-line check of the reference machine's 538 turns: at 0.59 T and their gap this formula predicts the required current within a couple percent if the H-frame iron is unsaturated; a measured efficiency well below ~95% signals a saturated or gappy flux path.

production of a field of 1 T in a gap with a 0.02 m spacing requires 16-kA turns (160 turns of wire if a 100-A supply is available).

Humphries, Principles of Charged Particle Acceleration (1986) — p. 111

Tabletop: Numerically the same worked example the builder needs: their 538 turns at ~30 A across ~5 cm predicts ~0.4 T ideal - the shortfall vs measured maps the iron's contribution.

Ampere-Turns = 2.02 x gauss x inches gap

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Tabletop: Directly applicable; e.g. 5900 G x 2 in gap needs ~24,000 A-turns before iron reluctance and leakage corrections.

the magnetic field actually increases in magnitude out to around r = 5 cm at which point it begins decreasing again. This is problematic because it yields a negative field index

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 51-53

Tabletop: A concrete trap when adding any iron or coil near the center of an 8-inch pole; check the sign of dB/dr everywhere, not just at the edge.

the difference in radius is minimal - about 0.2 cm - and comes at the steep cost of a ~20% reduction in maximum magnetic field from 1.27 T to 1.07 T. As such, this modification was considered insufficient.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 53-54

Tabletop: Saves a next machine's builder from spending months on trim coils inside a small gap; also note trim coils steal gap height.

the maximum field is limited by available water cooling and the power supply... To achieve the maximum field, using 70 A, the magnet requires 6.1 L/min

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 35-36

Tabletop: Do the L/min bookkeeping for the whole next machine (magnet + diffusion/turbo + RF amp) before buying a chiller; the cooling loop is a first-class design constraint, not an afterthought.

With the chamber in place, the separation between the pole tips is 3.81 cm, giving a maximum magnetic field of 1.28 T at 70 A ... requiring 18 C water flowing at 0.8 gallons per minute (at 50A)

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 2-3

Tabletop: A purchasable-magnet benchmark almost exactly at the reference machine's scale; the 0.8 gpm figure sizes a chiller for a ~kW-class coil.

The magnet's upper and lower coils are independently energized enabling an intentional axial field imbalance so as to vertically shift the accelerating plane.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 2

Tabletop: Cheap beam-height trim for a next machine: two supplies (or a shunt rheostat on one coil) instead of re-machining anything.

Trim coils increase the gap ... Very weak except in superconducting machines ... Model it before implementing it to avoid unexpected effects

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 33, 47

Tabletop: Settles the shim-vs-trim-coil question for a small warm magnet the same way the Houghton thesis did empirically: iron wins.

the field B = mu0 nI/h is proportional to the total current in the solenoid, is inversely proportional to the magnetic gap and is independent on the pole surface, a rather counter-intuitive fact to most people.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 70-71

Tabletop: The core sizing identity for a home magnet: shaving the pole gap buys field for free, whereas making the poles bigger does not.

By means of auxiliary coils wound on the pole pieces it is possible to control the position of the beam with respect to the median plane of the tank.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35

Tabletop: Directly applicable and cheap for a next machine: a few dozen turns on one pole with a bipolar bench supply gives a knob for vertical beam centering instead of mechanical re-shimming.

power varies inversely with volume of conductor, so to a first approximation it can be chosen at will ... a well-designed coil will have a 'packing ratio' greater than 0.5.

Livingston & Blewett, Particle Accelerators (1962) — p. 273-277

Tabletop: If a next machine's coils run hot, the fix is more copper, not more cooling: doubling conductor volume halves dissipation at the same ampere-turns.

The voltage breakdown strength of a resin-impregnated layer of glass cloth or cotton mesh is usually over 100 volts/mil ... necessary to utilize mica-sheet or mica-flake insulation to obtain the higher voltage-to-ground insulation.

Livingston & Blewett, Particle Accelerators (1962) — p. 278

Tabletop: Potting the reference machine's coils stops the slow insulation abrasion that coil hum causes; their low coil voltage means the resin-glass numbers alone give ample margin.

The conductivity is maintained at 10 micromhos or less, with a pH of about seven. Dee system water temperature stability of 1 F or better is required for steady operation.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6

Tabletop: Two directly portable specs: DI-water loop quality for any hollow-conductor coil, and tight dee-water temperature control if a next machine water-cools the dee.

The circulating pumps and heat exchanger are sized to handle a 1000-kw heat load, with the normal operating load being about 300 kw.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6

Tabletop: For a next machine dissipating ~1-5 kW, buy the chiller/radiator rated for ~3x that; margin is what makes long runs boring.

It is necessary for the secondary coil to be cooled with oil or deionized water... because even minute thermal expansion of the copper can change the inductor's value.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 23

Tabletop: Explains RF drift during long runs at the reference machine's power levels; cooling the tank coil stabilizes tune.

When properly cooled, our 1/4''x1/4'' hollow copper conductor can safely carry up to 120A. Allowing a margin of safety, we designed our magnet to operate at 110A.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Tabletop: Direct conductor rating for the exact class of hollow-conductor coil a next machine would use in place of the reference machine's refrigeration tubing.

Using this type of winding allows for a more uniform field than a simple spiral winding.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32-33

Tabletop: The reference machine's 538 turns of copper tubing could be rebuilt as ~10 potted double-pancakes per pole with a cooling manifold, easing fabrication and repair.

Our magnet can achieve a maximum temperature of 173 oF and will normally operate at no more than 142 oF.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 33

Tabletop: Sets the thermal design point for any potted coil in a next machine; consistent with Tanabe's <30 C rise rule for long potted-coil life.

The value of number of turns (N) is chosen to match power supply and interconnection impedances.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 35-36

Tabletop: The reference machine's 538 turns were set by their supply; for a next machine, pick the surplus supply first, then wind N = NI_required/I_supply.

Power distribution cables... are generally limited to a current density of <1.5 to 2 Amps/mm2.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 21

Tabletop: The go/no-go line for whether a next machine's coil design can skip water cooling: at or below ~1.5 A/mm^2 in the copper, air cooling can suffice.

the optimum is flat and appears to be j=4 Amps/mm2. However, a higher design value (the canonical j=10 Amps/mm2 value) is generally chosen.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 29-30

Tabletop: For a home machine where power cost matters and coils are hand-wound, the ~4 A/mm^2 end of the range is the better choice; the reference machine's tubing coil runs even lower.

f = 64/Re for laminar flow Re < 2000. For turbulent flow (Re>4000), the friction factor is gotten by solving a transcendental equation.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 32-34

Tabletop: The complete hydraulic sizing recipe for any hollow-conductor or tubing-wound coil at the reference machine's scale.

Desirable temperature rise... < 10 deg. C. Maximum allowable temperature rise (assuming 20 deg. C. input water) < 30 deg. C for long potted coil life.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 40, 45

Tabletop: One-line flow-rate calculator: a 1 kW coil on a next machine needs ~0.4 gpm for a 10 C rise.

For water velocities > 15 fps, flow vibration will be present resulting in long term erosion of water cooling passage.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 42

Tabletop: Hard upper bound when the builder sizes pump and passage diameter for a next machine's hollow-conductor coil.

Pressure drop can be decreased by a factor of eight if the number of water circuits are doubled.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 47

Tabletop: Argues for manifolded pancake sub-coils on a next machine instead of one long series water path through 538 turns.

If the design hole diameter is increased, the required pressure drop is decreased dramatically. If the fabricated hole diameter is too small... pressure drop can increase substantially.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 48

Tabletop: When choosing hollow conductor for a next machine, err to the larger bore; also a reason to flow-test each pancake before potting.

A single water circuit in a coil assembly should be wound from a single continuous length of conductor. Splices 'buried' within the potted insulation should not be allowed.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 14-16

Tabletop: For a next machine wound from copper refrigeration tubing: buy one continuous coil per water circuit, keep the shop swarf away from the winding, and verify the bore is clear before the tubing is buried in the stack.

A sick coil will exhibit waveforms whose frequency and/or damping rate changes as the voltage increases or will exhibit hash at the peak of the damped sinusoid.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 17-24

Tabletop: A signal generator, capacitor and scope let the builder certify the next machine's coils before they are trapped under the yoke; also hipot potted coils at 2x operating voltage + 1 kV with < 2 mA/kV leakage.

Water flow calculations made for the preliminary design may be unreliable for a coil designed with many tight turns... due to the added flow impedance of tight radius turns.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 25

Tabletop: The reference machine's 538-turn tubing coil is exactly the many-tight-turns case; a bucket-and-stopwatch flow test at operating pressure is the real spec, not the straight-pipe pressure-drop formula.

Water hoses should be at least one meter long and use nonconducting material to prevent current leakage from the magnet.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 3

Tabletop: The reference machine's water-cooled copper-tubing coil sits at supply potential; a meter of plastic hose per lead and interlock-on-return are exactly the cheap practices that prevent shocks and detect a blocked circuit at home scale.

The normal set-point of Klixons is about 89 C... One thermal interlock is installed on each water circuit.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 5-6

Tabletop: A $5 thermal snap-switch soldered to the coil exit tube, in series with the magnet supply enable, is the single best protection against cooking the next machine's winding on a lost-water event.

Inter-turn insulation thickness is normally between 0.3 mm and 1.0 mm, the ground insulation thickness should be between 0.5 mm and 3.0 mm depending on the applied voltage.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 28-29

Tabletop: Sets realistic packing-factor expectations for a hand-wound 538-turn coil and how much window the insulation eats.

For a bending radius of three times the conductor width we can expect a keystoning of 3.6% ... we can ignore the effect of keystoning by systematically choosing a bending radius four times larger than the conductor width.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 30

Tabletop: Directly applicable to bending copper tubing for a 538-turn homemade coil: tight bends also pinch the cooling bore and risk insulation damage.

An aspect ratio of c:b between 1:1 and 1:2 should be chosen, and the packing factor fc somewhere between 0.6 and 0.8.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Tabletop: Turns the amp-turn number into an actual coil window size before you buy tubing or start winding.

This implies that for a given flow, the pressure drop is reduced by a factor of eight by doubling the number of cooling circuits.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Tabletop: Explains why splitting a big coil into 2 or 4 hydraulic circuits lets a modest garage chiller pump do the job.

Water resistivity higher than 0.1x10^6 Ohm m; pH-value between 6 and 6.5; dissolved oxygen below 0.1 ppm

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 34

Tabletop: If a next machine uses water-cooled coils at high voltage, tap water will leak current and corrode; a small DI cartridge loop is the fix.

power distribution cables are convectively cooled and are limited to <= 1.5 Amps/mm2

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 128-129

Tabletop: The reference machine's copper-tubing winding at 538 turns: if any leg of the circuit (bus, jumper, lead) runs above ~1.5 A/mm^2 without water flow it will run hot; size leads accordingly.

Normally, a good value for the current density is j = 10 Amps/mm2 for water cooled coils... The value of the packing fraction is typically f ~ 0.5 for small conductors.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 129

Tabletop: Lets the builder size a next machine's coil cross-section on one sheet of paper: gross coil area ~ NI/(j*f) = NI/5 in mm^2 for water-cooled copper.

Flow velocity v <= 4 m/sec to avoid flow vibration and erosion... An acceptable coil temperature rise which protects the coil epoxy encapsulation from damage is dT <= 30 C.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 134-135

Tabletop: Direct water-cooling design window for a next machine's hollow-conductor coil; also warns that a lazy laminar-flow circuit cools far worse than the handbook film coefficient suggests.

Kilowatt-Tons = (0.118)Cu (Mega-ampere turns)^2 (inches mean turn length)

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Tabletop: Directly applicable trade study tool: the product of coil dissipation and coil weight is fixed by NI and geometry, so more copper always buys less heat.

The coils should be wound so that they occupy approximately a rectangular cross section around the poles ... Either too flat or too tall a coil intercepts more leakage flux and thus wastes turns.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable guidance for a next machine's coil geometry.

operate close-wound naturally air-cooled coils at a current density not exceeding 750 amps per square inch of conductor area. For intermittent operation this may be raised to 1000 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable thermal sizing rule for a next machine's magnet coils.

Most coil designs favor large conductor areas and correspondingly high amperages; this reduces total voltage and simplifies both the insulation and the winding problems.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable when choosing wire gauge and supply for a next machine's coils.

flat donuts of 1/16 in. copper sheet ... having a 1/4 in. copper pipe soldered to the outer edges ... such coils should operate steadily at 1300 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 4

Tabletop: Directly applicable cheap upgrade: 1/16-inch copper donut plates with soldered edge tubing between pancakes nearly doubles allowable steady excitation.

These windings saturate the iron (~20 KG) at somewhat less than ten amperes; at this current the temperature becomes excessive in less than an hour

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 4

Tabletop: Directly applicable cautionary datum: quote coil ratings as (current, time-to-overheat) pairs, not just maximum field.

The magnet coil circuit must never be broken at high currents, of course, unless adequate surge protection is provided.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 5

Tabletop: Directly applicable; a next machine with tens of henries of coil inductance needs a freewheel diode/varistor dump path or it will arc its switchgear.

The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3

Tabletop: Concrete LC numbers for a next machine's tank at the same scale; the swappable-primary approach lets you retune coupling without rebuilding the tank.

An alarm warns the operator when the coil temperature has reached a predetermined value, usually 70 to 80 C ... one to three hours are required for the temperature to reach equilibrium.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 33

Tabletop: Directly applicable: put a thermocouple in the next machine's winding and log it; a coil that is fine at 30 minutes can still cook at 2 hours.

It is important for the coils should be in the air stream of one of the cooling fans (they will run hot if not).

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 28

Tabletop: Directly applicable to the homemade dee-tank coil, which sees circulating RF current far above the dee's DC feed current.

This operated normally at 65 C but when an identical coil, which had been nickel plated, was substituted, the operating temperature rose to 350 C.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 4

Tabletop: Reject nickel-plated hardware (and nickel underlays beneath chrome or silver) anywhere RF current flows in the resonator, coil, or ground-return path.

Most commercially available copper tube contains 0.015% to 0.08% phosphorus as a de-oxidising agent, so that its conductivity may range from 60% to 90% I.A.C.S.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 6

Tabletop: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper, not generic plumbing tube, for up to ~20% lower RF resistance.

typically have true Q values of up to about 800. Very few practical circuits require a Q above 900. Attempting to design a coil with a True Q much over 1,000 usually results in a coil with abnormal physical dimensions

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Tabletop: Budget the resonant step-up assuming coil Q of a few hundred (loaded lower still), not textbook thousands, when sizing the amplifier for 5-13 kV dees.

the presence of the coil's distributed capacity causes the Q observed by the Q meter to be lower than the true Q of the coil

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Tabletop: When characterizing the dee resonator with a VNA or Q meter, treat the reading as a lower bound and keep leads/fixture capacitance minimal.

Q increases with coil diameter (see figs. 1-4). Q increases with coil length, rapidly when the L/d ratio is small ... Q increases with frequency

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1-2

Tabletop: At 9 MHz a 3-4 inch diameter tank coil can reach Q well over 1000, directly multiplying dee voltage per watt of drive.

The conductor diameter must be within the range of 0.45 and 0.70 times the center-to-center distance between adjacent turns (not all commercial stock coils meet this condition).

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2

Tabletop: For a 9 MHz matching/tank inductor, space the turns so the wire fills 45-70% of the pitch; close-winding bare tubing throws away Q to proximity effect.

Maximum Q occurs at a coil L/d ratio of between (depending on other coil design parameters) 0.35 and 0.45, decreasing rapidly below that ratio and more slowly above

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2-3

Tabletop: Make the resonator coil short and fat (roughly half as long as its diameter), not the long skinny solenoid that fits most easily in a corner.

The equations do not hold for coils with a length-to-diameter ratio of less than 0.35:1, coils with less than about 4 turns, or coils with conductor diameter-to-turn spacing ratios of less than 0.45:1 or greater than 0.70:1.

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 3

Tabletop: A 2-3 turn link or coupling loop at 9 MHz is outside the formulas; measure it rather than calculate it.

The practically achievable engineering current density (the ratio of the value of the ampere-turns in the winding to the cross section of the conductor) is of the order of 5 A/mm2.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 15-16

Tabletop: Direct sizing rule for a next machine's coil packs: total ampere-turns / 5 A/mm^2 gives the minimum copper cross-section with water cooling; air-cooled magnet wire should be derated well below this.

The coil height giving the minimum cost was found for a field of 20,000 gauss. Since the cost curve had a flat minimum this resulted in little increase in cost.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 8

Tabletop: General magnet economics, transferable - pick a next machine's coil proportions near the cost/power optimum, then adjust freely for winding or cooling convenience.

Glass tape is inserted along all metal seams to prevent weld-flash from entering the can.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 14

Tabletop: Directly applicable craft rule for any welding or brazing done near a next machine's coil insulation or on the coil case.

requires the addition of an inhibitor to reduce attack on the aluminum and steel provoked by the presence of minute quantities of copper in the water.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 53

Tabletop: Directly applicable chemistry for any next machine's water loop touching Cu plus Al; use a modern inhibitor (chromate is toxic/regulated today).

All the adapters on the coil terminals are water cooled and supplied with thermal switches to protect the coil terminals from overheating.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 56

Tabletop: Directly applicable - thermal cutouts on a next machine's coil terminals/lugs (and dee stem cooling) are cheap insurance against a loose-joint meltdown.

Weight, Fe 6 ; Cu 4 tons. Winding 3/4 in x 1/16 in strip.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 106

Tabletop: Extrapolating down, an 8-in-pole machine wants ~0.5-1 ton of iron - hobby-crane scale; it also warns that every inch of extra pole diameter on a next machine is bought with steeply growing steel.

Air-cooled coils. Iron ore blocks for shielding

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 127

Tabletop: Supports keeping a next machine's coils air-cooled with duty-cycle management instead of plumbing water - two real machines at 12.5-16 kG did exactly that.

The resistance of the coil is proportional to its mean circumference ... the coil should be as small as is consistent with a reasonable power requirement.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 25

Tabletop: The compounding is the point - on any H-frame rebuild, fat coils cost twice (copper AND the longer steel circuit around them), so invest in space factor and cooling before adding turns.

In a high-current low-voltage coil, insulation is required only to maintain mechanical separation of the conductors.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 25

Tabletop: Argues for the classic amateur choice - few turns of heavy bar/strap at high current with generous cooling passages beats many-turn fine-wire coils on space factor, insulation risk, and pumping pressure.

A second type of coil which is more attractive, when the coil must be wound at the cyclotron site, is a flat-wound helix.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 26

Tabletop: Directly a garage-scale construction technique - cut flat copper sectors, stack into a helix with brazed/bolted joints (see the 10 kA/cm2 joint rule), no winding mandrel needed.

The costs which are affected are the combined costs of steel, copper, and energy.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30-32

Tabletop: This collection's only explicit dollar-optimization of magnet proportions - rerun Eq. 114 with 2026 unit costs (scrap steel, surplus copper, $/kWh over expected machine life) to place a next machine's coil proportions. NYO-780 p.8 did the equivalent sweep by model; cite both.

For operating convenience, the coils should be made smaller than is indicated because the total cost is a slowly varying function of the coil outside diameter near the minimum of cost.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Tabletop: Licence to trade a few percent of cost-optimality for access, cooling clearance, or stock material sizes - the optimum is a plateau, not a peak. Same flat-minimum finding as NYO-780 p.8 (coil height); cite both.

It appears that the unit costs can only be determined after the cyclotron has been in operation for several years, so estimates must be employed.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Tabletop: A 1952 statement of the plan's own doctrine - cost models are gated on real operating data, so freeze the estimate, build, and revise with actuals rather than polishing the spreadsheet.

It is quite clear from either equation that this factor, optimum x, depends on scale factor. The assumptions made cause the value of x given by the equation to be too large.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 31

Tabletop: Two cautions in one - shave the computed OD, and treat big-machine coil proportions (including TID-454's own x~1.4) as non-transferable to an 8-12 in machine without redoing the optimization at that scale.

One square centimeter of metallic contact distributed over the joint will carry 10,000 amps with negligible resistance and temperature rise.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 32

Tabletop: Frees a builder from soldering anxiety on bus joints - a clean bolted lap of a few cm2 is electrically invisible at the tens-to-hundreds of amps any amateur coil carries.

The generator should match the coil in the sense that the quotient of the maximum voltage output and the maximum current should be equal to the resistance of the coil.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33

Tabletop: When sizing a surplus supply for the next machine's coil (or the number of turns for a given supply), pick turns so the coil's hot resistance sits at the supply's V_max/I_max corner.

the field obtained is proportional to the inside radius of the coil and a high field can be obtained by increasing the scale ... the power p and the volume of conductor v increase with the cube of the inside radius.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 116

Tabletop: SCALE-SCOPED (megagauss context) but the scaling itself is exact and explains amateur economics - it is why small bore air-core inserts and compact analyzing magnets are feasible while whole-machine air-core fields are not.

For fields of 10^5 gauss and above, the situation is quite different; the power and maximum current density become important factors and more complicated designs are useful.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 122

Tabletop: Locates amateur work far below the exotic regime - for sub-kG correction coils, steering windings and test solenoids, wind the simple thing; sophistication buys nothing until iron saturates and fields climb an order of magnitude.

Helmholtz coils have cross sections small in comparison with their radii squared, and thus require excessive power where a high field is required.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 108

Tabletop: Marginal for the cyclotron itself, but the right doctrine for any air-core uniform-field fixture - probe-calibration coils, a beamline corrector, or a small synchrotron's reference field - when tens of gauss or more are wanted continuously.

One of these coils consists of an insulated conductor wrapped half-way around the magnet pole piece and attached so that the pole piece completes the circuit.

Howard (ed.), Electromagnetic Research Division Semiannual, period ending 20 March 1953 — ORNL-1531 (1953) — p. 18

Tabletop: 86-inch numbers, but the trick scales - a few-turn half-wrap trim coil on a next machine's pole gives a first-harmonic/gradient control for orbit centering and effective-energy variation that FEMM can model directly; also a candidate cheap "variable-energy" feature for an educational machine.

This low field avoids saturation difficulties in the magnet iron and high excitation power requirements. Furthermore, it enables us to dispense with water cooling in the windings.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 30

Tabletop: DIRECT - at a next machine's rigidity, transport-quad fields are hundreds of gauss at most, so air-cooled random-wound coils on unsaturated iron are the default. OCR trap - the text layer renders the B^1/2 exponent as B^2; page image verified B^1/2.

the coils in each unit are connected in series since otherwise we would have extreme difficulty in maintaining uniform gradients.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 31

Tabletop: DIRECT wiring doctrine for any home-built multipole - gradient symmetry comes from forced equal current, not matched resistances. The 20% ampere-turn margin and the use-the-wire-you-have coil design (surplus

the quantity (NI)g represents 85 to 95 per cent of the total mmf required (i.e., the efficiency ranges from 85 to 95 per cent), and Eq. 7 can be used to give a useful first approximation

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 21

Tabletop: Same arithmetic every H-frame designer runs today (corroborates the ampere-turn sizing in Wouters and Zickler's CAS magnet notes); the 85-95% efficiency band is a sanity check on any FEMM excitation result for an unsaturated return frame.

the product of the power and weight of a coil conductor depends on the ampere turns and the mean diameter of the coil.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Tabletop: The cleanest statement in this collection of the copper-vs-power trade: double the copper, halve the dissipation, at fixed NI. Lets a coil be resized on one line when a surplus supply or a heat limit is the binding constraint.

For continuous operation, 1600 amp/sq in. is about the upper limit used for oil-cooled coils. This compares with 1000 amp/ sq in. for open bus bars cooled by free convection

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Tabletop: Brackets the usual 1.5-2.5 A/mm^2 air-cooled small-magnet guidance from the modern side (Zickler/Tanabe territory) with 1940s operating experience; a passively cooled tabletop coil should sit at or below the bus-bar figure.

Two experimental models had values of 0.37 and 0.30, but in both cases it was necessary to use conductor sizes which were available but not specifically designed for the job.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Tabletop: Amateur coils are almost always wound from available magnet wire — budget the pessimistic 0.3-0.4 space factor, not the textbook 0.5, when sizing the coil window.

Force between pole faces (lb) = 1/1.735 X (kilogauss)^2 X area (sq in.)

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 31

Tabletop: The 1.735 pole-force constant is the imperial twin of B^2/2mu0 and matches it to 1%; the hot-spot width formula is a one-line check before winding wide flat strip on a driver-amplifier-fed coil.

It was found that when the number of turns on the end coils was 50 per cent of a full coil, the field in tanks adjacent to the yokes was 4.0 per cent low.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 139

Tabletop: The general pattern — a boundary cell needs measured, adjustable over-excitation (or shimming), and a two-point measurement plus linear extrapolation converges in one iteration — applies to any edge-compensation knob: outer-radius shim thickness, trim turns near a yoke window, or a correction-coil ampere-turn setting.

the supporting structure for the coils failed, presumably under the magnetic forces. The coils became distorted and short circuits developed.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 19

Tabletop: DIRECT at any scale: coil-on-coil and coil-on-iron forces scale with NI and B and have crushed amateur windings. Brace windings as if they will be pushed, and remember the yoke-steel trick — outer return-path steel raises gap field without touching pole-gap geometry.